Tut sol week9 - BES Tutorial Sample Solutions, S1/11 WEEK 9...

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1 BES Tutorial Sample Solutions, S1/11 WEEK 9 TUTORIAL EXERCISES (To be discussed in the week starting May 2) 1. Perform the following hypothesis tests of the population mean. In each case, illustrate the rejection regions on both the Z and X distributions, and calculate the p-value (prob-value) of the test. (a) H 0 : μ = 50, H 1 : μ > 50, n = 100, ݔҧ = 55, σ = 10, α = 0.05 Rejection region: ݖൌ ݔҧെ50 10 √100 ൐ݖ ଴.଴ହ ൌ 1.645 Alternatively ݔҧ൐ݔҧ ൌߤ ൅ݖ ଴.଴ହ ߪ ݊ ൌ 50 ൅ 1.645 ൬ 10 √100 ൰ ൌ 51.645 Since ݖൌ 55 െ 50 10 √100 ൌ5൐ݖ ଴.଴ହ ൌ 1.645 Can reject 0 H and conclude that the population mean is greater than 50 . 0.05 X 50 51.645 reject
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2 0.05 0 1.645 Z reject ݌ െ ݒ݈ܽݑ݁ ൌ ܲሺܼ ൐ 5ሻ ൎ 0.0000 (b) H 0 : μ = 25, H 1 : μ < 25, n = 100, ݔҧ = 24, σ = 5, α = 0.1 Rejection region: ݖൌ ݔҧെ25 5 √100 ൏ݖ ଴.ଵ ൎ െ1.28 Alternatively ݔҧ൏ݔҧ ൌߤ െݖ ଴.ଵ ߪ ݊ ൌ 25 െ 1.28 ൬ 5 √100 ൰ ൌ 24.36 Since ݖൌ 24 െ 25 5 √100 ൌെ2൏െݖ ଴.ଵ ൌ െ1.28 Can reject 0 H and conclude that the population mean is less than 25 . 0.1 X 24.36 25 reject
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3 0.1 ‐1.28 0 Z reject ݌െݒ݈ܽݑ݁ൌܲሺܼ൏െ2ሻ ൌ 0.0228 (c) H 0 : μ = 80, H 1 : μ 80, n = 100, ݔҧ = 80.5, σ = 4, α = 0.05 Rejection region: ݖൌ ݔҧെ80 4 √100 ൏െݖ ଴.଴ଶହ ൎ 1.96 ݋ݎ ൐ 1.96
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This note was uploaded on 05/24/2011 for the course ECON 1293 taught by Professor Denzilgfiebig during the Three '11 term at University of New South Wales.

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Tut sol week9 - BES Tutorial Sample Solutions, S1/11 WEEK 9...

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